Spin injection across a hybrid ferromagnet/semiconductor junction has proven to be difficult, unlike in an all-metal junction used in giant magnetoresistance devices. The difference responsible is highlighted in a simple model. We perform spin-injection-detection experiments on devices with two ferromagnetic contacts on a two-dimensional electron gas confined in an InAs quantum well. We demonstrate that spin injection allows the hybrid device to combine both the advantage of the ferromagnet as well as that of the semiconductor.